Phillips N.Ch. — Equivariant K-Theory and Freeness of Group Actions on C*-Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Phillips N.Ch. — Equivariant K-Theory and Freeness of Group Actions on C*-Algebras

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Название: Equivariant K-Theory and Freeness of Group Actions on C*-Algebras

Автор: Phillips N.Ch.

Аннотация:

This book is based on the author's Ph.D. thesis written at the University of California at Berkeley. However, it incorporates substantial revisions and many additional results. The research reported here has been partially supported by a National Science Foundation Graduate Fellowship, by the Mathematical Sciences Research Institute (NSF Grant 8120790). and by a National Science Foundation Postdoctoral Fellowship. All of this support is gratefully acknowledged. Thanks are also due to Marsha Colby, who converted an enormous number of sometimes rather illegible handwritten pages into the computer files from which this manuscript was produced, and who, with rare exceptions, was able to persuade a University of California computer to print many symbols that it had never been intended to make.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1987

Количество страниц: 371

Добавлена в каталог: 17.04.2008

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Предметный указатель

Representation, complex conjugate      39 71 109 155 323—324
Representation, covariant      16 17 43 51—52 135 283
Representation, induced      175 see
Representation, integrated form      17 38—39 43 51—52 135 198 238 241 283
Representation, irreducible of C*-algebra      280 283
Representation, irreducible of group      19 41 47 65
Representation, multiplicity of      60 71 133 299
Representation, normal      283
Representation, projective unitary      48 138 140 154 232 280 289
Representation, regular, of $L^{1}(G,A,\alpha)$       209
Representation, regular, of group      39 60 65 70 133 164 172 213 258 259 261 264 283 292—298 302 306 316
Representation, ring      13—14
Representation, universal      70 109 111 114 160 172
Res (= $Res^{G}_{H}$ )      168
Resolution, free      202
Resolution, projective      2l5 2l7 220
Restriction map in K-theory      8 167 168—170 177—180 231 294—290
Restriction map in KK-theory      167 171—173 176—177 181 182 320—323
Restriction map in representation rings      10 64 144 146 149 168—170 177—180 182 200 229—231 259 305 321 327
Restriction of action to subgroup      3—5 137—138 143 162 167 177—182 185 272 282 288 294 299—309
Restriction of action to subgroup and K-freeness      137—138 167 282 294 302—305
Restriction of action to subgroup and KK-freeness      4 167 185 233 307
Restriction of action to subgroup and locally discrete K-theory      178 182 294
Restriction of action to subgroup and total K-freeness      138 167
Rieffel, M.A.      2 23 42 43 66 117 236 237 239 240 243 244 263
Rosenberg, J.      3 12 68 189 208 242 285 305 325
Rossmann, W.      286 292 294 297 298 305
Rotation algebra, irrational      263—265
Rubinsztein, R.L.      179
S(B) (semigroup of idempotents)      36
SA (suspension)      51
Saturated action      236—237 240—251 270 273—274 282
Saturated action, hereditarily      236—237 246—251 270—275 278 281—285 299—301
Saturated Banach *-algebraic bundle      240 244
Schochet, C.      4 61 67 68 144 156 184 189 190 196 197 200 201 203 205 208 209 213 214 215 216 217 218 219 267 268 270 305 325
Second dual of C*-algebra      70 283
Segal, G.B.      1 6 7 8 10 12 13 14 17 64 132 139 144 149 167 179
Separated point      149
Separated sets      254—257
Serre, J.-P.      167 177 180 292
Sheaf cohomology      114
Sheaf of C*-algebras      157 see
Similarity      31—32 34 37—38 42
Simple C*-algebra      4 137—138 140 244 251 258 261—266 268 272 279 282 284 291 295 2918—301 313
Simple C*-algebra, G-      141 252 261 270 310 313 324 326
Singer, I.M.      12 113 115
Skandalis, G.      69 121 125
Sobolev chain (discrete)      111
Sobolev space      111—112 114
Sp( $\alpha$ ) (Arveson spectrum)      246
Spatial isomorphism      71—72 109
Spectrum, Arveson      137—138 246 249 301
Spectrum, Connes      4 131 137—138 236 249 250 263—264 282 301 305
Spectrum, strong      246 249—250
Spectrum, strong, Connes      4—5 212 227 236—237 249—250 257—263 283 286 305
Split prequasihomomorphism      99—100 102—103
Stability of equivariant K-theory      46 53—54
Stability of equivariant KK-theory      109
Stability of K-freeness      140
Stability of K-theory (ordinary)      48 66
Stability of KK-freeness      155
Stability of total K-freeness      140 180 288—289
Stabilization theorem      117 119 121 122
Stable C*-algebra      208
Stable isomorphism      66 201 267 270
Stably finite      252—253 261 264 266 270
Stammbach, U.      202 220
State      42—43
Steenrod, N.      144
Stormer, E.      137
Strict topology      44—45 117—120 122 158
Strictly positive element      325
Strong Connes spectrum      4—5 212 227 236—237 249—250 257—263 283 286 305
Strong Morita equivalence      4 66 236—239 243—244 285 298
Strong operator topology      16 24 46 207 280
Strong spectrum      246 249—250
Subquotient      142 147 251—261 266 270 273—274 279—282
Subquotient, G-invariant      251 254 256—261 274 279—283
Support (of a prime ideal in R(G))      10 139 149—151 163 179 189 200 213 215—221 229 231 232 281
Suspension of C*-algebra      51
Suspension of space      7
Swan's Theorem      12 15 22—23 111
Swan, K.W.      23 24 26
SX (suspension)      15
Symbol (of a pseudodifferential operator)      112 116
System of imprimitivity      66 183
System, multiplicative      6 152 272 293
Takai duality      60 164 213 258 264 283 316
Takesaki, M.      104 140 159 191 234 284
Taylor, J.L.      3 12 57 58 59 61 110 117
Tensor product of C*-algebras, action on      70
Tensor product of C*-algebras, algebraic      197
Tensor product of C*-algebras, equivariant K-theory of      4 67 189—190 200 215 218—221 229—233 235
Tensor product of C*-algebras, K-freeness of actions on      140 143 144—145 229 234—235
Tensor product of C*-algebras, K-theory of      144 189 201—202 209 267—268
Tensor product of C*-algebras, K-visibility of      267—270
Tensor product of C*-algebras, KK-freeness of actions on      154—155 233
Tensor product of C*-algebras, maximal      159 234
Tensor product of C*-algebras, minimal      104 191
Tensor product of C*-algebras, total K-freeness of actions on      4 140 143 144—146 148 164 180 190 230 232 288—289 291

Tensor product of graded modules      191
Tensor product of Hilbert spaces, action on      70
Tensor product of vector bundles      13
Tensor product of vector bundles, action on      13
Tensor product of vector bundles, external      129 189
Tensor product theorem      230 232 234 291
Tietze extension theorem      162
Tomiyama, J.      120 122 140
Topologically cyclic group      10
Tor      202 218 220 231 267 268
Tor (derived functor of $\otimes$ )      202
Total K-freeness      3—5 131 138—148 151 156—157 162—165 167 179—181 185—186 189—190 211—213 229—234 236 251 263—265 275 278 282 285 286 288—289 291 294—295 299 302 306—309 312—313 326
Total K-freeness and $C_{0}(X)$ -algebras      131 162—164
Total K-freeness and actions with (totally) K-free restrictions      4 143 167 179 181 288
Total K-freeness and AF actions      5 286 288—289 291 302 307 308—309 312 see
Total K-freeness and bundles of C*-algebras      146
Total K-freeness and commutative algebras      138
Total K-freeness and composition series      141—142
Total K-freeness and crossed products by $F_{n}$       213
Total K-freeness and crossed products by R      213
Total K-freeness and crossed products by Z      212
Total K-freeness and direct limits      141
Total K-freeness and extensions      138
Total K-freeness and exterior equivalent actions      139 141 212
Total K-freeness and free action on the primitive ideal space      3 5 151 278 282 299
Total K-freeness and hereditary saturation      236 263
Total K-freeness and hereditary subalgebras      141 142
Total K-freeness and ideals      138
Total K-freeness and K-freeness      137—138 234 302—305
Total K-freeness and KK-freeness      157
Total K-freeness and locally representable actions      294—295
Total K-freeness and product type actions      299
Total K-freeness and quotients      138
Total K-freeness and restrictions of actions to subgroups      136 167
Total K-freeness and stably isomorphic algebras      140 180 288—289
Total K-freeness and strong Connes spectrum      236 263
Total K-freeness and tensor products      4 140 143 144—146 148 164 180 190 230 232 233 288—289 291
Total K-freeness and twisted products      146—148
Total K-freeness and type I algebras      5 275 278 282 285
Total K-freeness up to torsion      178—179
Totally disconnected space      309
Totally positive element of $K_{0}(A)$       251—252 256—257 259—260 266—269 294
Trace      264
Twisted product of algebras      64
Twisted product of algebras, characterization of (for discrete groups)      66
Twisted product of algebras, equivariant K-theory of      64—66
Twisted product of algebras, equivariant KK-theory of      320—323
Twisted product of algebras, induction in KK-theory and      171—174
Twisted product of algebras, K-freeness of      146
Twisted product of algebras, locally discrete K-theory and      146
Twisted product of algebras, spaces and      64
Twisted product of algebras, system of imprimitivity and      66 163
Twisted product of algebras, total K-freeness of      146—148
Twisted product of algebras, transitivity of      171
Twisted product of spaces      64
Two-cocycle      155
Type I algebra      5 134 201 206—200 215 219 227—228 232—233 252 268—271 274—285 299 300 302
Type I algebra and K-freeness      5 275 281
Type I algebra and KK-freeness      278—279
Type I algebra and locally discrete K-theory      134—136
Type I algebra and total K-freeness      5 275 278 282 285
UHF algebra      286 292—294 297—302 305 309
Uniform boundedness principle      25 38
Unitary equivalence      31
Unitization      22
Unitization, free      131 164
Universal coefficient theorem      68 308
Universal enveloping von Neumann algebra      70 283
Universal representation      70 109 111 114 160 172
Universally weakly inner automorphism      283—284
Unperforated ordered group      297
Valuation ring (discrete)      216
Vector bundle      2 6—8 12—15 23—27 110—115 129 156—157 189
Vector bundle, G-      6—7 13—15 23 26—27 129 189
Vector bundle, holomorphic      114
Vick, J.W.      156
Virtual dimension      14
Voiculescu, D.      190 209 210
Wasserman, A.J.      293
Weakly K-visible C*-algebra      273 see
Whitney sum      13
X/G (orbit space)      2
Z      see "Action of Z" "Crossed
Z/2Z      see "Action of Z/2Z" "Crossed
Z/2Z-graded group      191
Z/3Z      see "Action of Z/3Z" "Crossed
Z/4Z      see "Action of Z/4Z" "Crossed
Z/6Z      see "Action of Z/6Z"
Z/nZ      see "Action of Z/nZ" "Crossed
Z/pZ (p prime)      see "Action of Z/pZ (p prime)" "Crossed
Zero quasihomomorphism      79
Z[G] (group ring)      50
[ ] (equivalence class)      see "[E]" "[g "[p]" "[V]" " "
[E] (class of vector bundle in K-theory)      13
[E] (isomorphism class of vector bundle)      13
[g,x] (element of $G\times_{H}X$ )      64
[p] (class of idempotent in K-theory)      28
[V] (class of representation space in R(G))      14
| (divides)      see "d|n"
| (restriction)      see " $\alpha_{(\cdot)}|_{I}$ "

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